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Finding the Third Proportional to 82,098 and 177,021

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Solution

The third proportional to 82,098 and 177,021 is: 381,695.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,098 : 177,021 = 177,021 : x
  2. Step 2: Convert to fraction form
    82,098/177,021 = 177,021/x
  3. Step 3: Cross multiply
    82,098x = 177,021 × 177,021
  4. Step 4: Simplify right side
    82,098x = 31,336,434,441
  5. Step 5: Solve for x
    x = 31,336,434,441/82,098
  6. Step 6: Final answer
    x = 381,695.47

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.